Field of the Invention
The present invention relates to a planar optical waveguide element, a dual polarization quadrature phase shift keying modulator, a coherent receiver, and a polarization diversity.
Priority is claimed on Japanese Patent Application No. 2014-173320, filed on Aug. 27, 2014, the content of which is incorporated herein by reference.
Description of Related Art
Currently, the amount of information transmitted in optical communication is increasing. In order to respond to such an increase in the amount of information, measures have been taken for an increase in the signal speed, an increase in the number of channels due to wavelength multiplexing communication, and the like. In particular, in digital coherent transmission technology of the next generation 100 Gbps (gigabit per second) for high-speed information communication, in order to double the amount of information per unit time, a polarization multiplexing scheme for carrying information in two polarized waves having electric fields perpendicular to each other is used.
However, in modulation schemes for high-speed communication including the polarization multiplexing scheme, an optical modulator having a complicated configuration is required. For this reason, problems, such as an increase in device size and an increase in cost, occur. In order to solve such problems, an optical modulator including a planar optical waveguide using silicon, which is advantageous in terms of easy processing, size reduction by integration, and cost reduction by mass production, has been studied.
However, the polarization multiplexing in the planar optical waveguide has the following problems. In general, the planar optical waveguide has a shape in which the width direction parallel to the substrate and the height direction perpendicular to the substrate are asymmetric. For this reason, between two types of polarization modes of a mode in which an electric field component in the width direction is a main component (hereinafter, referred to as a TE mode) and a mode in which an electric field component in the height direction is a main component (hereinafter, referred to as a TM mode), characteristics, such as effective refractive indices, are different. Among these modes, TE0 and TM0 are used in many cases. TE0 refers to a mode having the largest effective refractive index of the TE modes, and TM0 refers to a mode having the largest effective refractive index of the TM modes.
It is difficult to perform an optical modulation operation for these modes having different characteristics with a single planar optical waveguide element. Accordingly, planar optical waveguide elements that are optimally designed for the respective modes are required. However, this requires a lot of effort in terms of the development of the planar optical waveguide elements.
As a method for solving this problem, a method can be mentioned in which TE0 is used as light incident on the planar optical waveguide element designed optimally for TE0 and the output is polarization-converted to TM0. The polarization conversion herein indicates a conversion from TE0 to TM0 or a conversion from TM0 to TE0. In order to perform the operation described above, a planar optical waveguide element for performing polarization conversion on the substrate is required.
As a technique for performing such polarization conversion on the substrate, there is a method of combining the conversion between TE0 and TE1 and the conversion between TE1 and TM0. Among these, focus will be given to the conversion between TE0 and TE1. Here, TE1 indicates a TE mode having a second largest effective refractive index.
As an optical waveguide element having a function of conversion between TE0 and TE1 in the related art, an optical waveguide element disclosed in Daoxin Dai and John E. Bowers, “Novel concept for ultracompact polarization splitter-rotator based on silicon nanowires,” Optics Express, Vol. 19, Issue 11, pp. 10940-10949 (2011) can be mentioned.
FIGS. 55A and 55B show an optical waveguide element obtained by modeling the structure disclosed in Daoxin Dai and John E. Bowers, “Novel concept for ultracompact polarization splitter-rotator based on silicon nanowires,” Optics Express, Vol. 19, Issue 11, pp. 10940-10949 (2011). FIG. 55A is a plan view, and FIG. 55B is a sectional view.
The optical waveguide element includes core regions 81 and 82 and a cladding 15. The cladding 15 includes a lower cladding 7 and an upper cladding 6.
The core regions 81 and 82 are straight waveguides, and are arranged in parallel to form a directional coupler. In the directional coupler, the TE0 of the core region 81 and the TE1 of the core region 82 are coupled to perform mode conversion.
In order to perform efficient mode conversion in the directional coupler, it is necessary to make the effective refractive indices of TE0 and TE1 be approximately the same. Therefore, the waveguide structure is adjusted according to the respective modes.
In the optical waveguide element, in order to make the effective refractive indices of TE0 and TE1 be approximately the same, the widths of the core regions 81 and 82 are adjusted. Since the widths of the core regions 81 and 82 are different, the directional coupler is referred to as an “asymmetric directional coupler”.
However, the optical waveguide element described above couples different modes. Therefore, even if the conditions “making the effective refractive indices of TE0 and TE1 be approximately the same” for a specific wavelength are satisfied by adjusting the waveguide structure (for example, by adjusting the width of the core region), the effective refractive indices of the two above modes are shifted in case that the wavelength is changed. In addition, when the waveguide structure is changed due to a manufacturing error, the effective refractive indices of the two modes are shifted. These may reduce the conversion efficiency.
Therefore, the related art has a problem that the wavelength band that enables high-efficiency conversion is narrow and the related art is susceptible to manufacturing errors.
Hereinafter, these problems will be described using the asymmetric directional coupler in the related art shown in FIGS. 55A and 55B as an example.
In this example, the core regions 81 and 82 are formed of Si (refractive index of 3.48), and both of the upper and lower claddings 6 and 7 are formed of SiO2 (refractive index of 1.44). The heights of the core regions 81 and 82 are set to 220 nm. The gap between the core regions 81 and 82 is set to 200 nm.
The waveguide including a narrow core region 81, through which the TE0 to be mode-converted is guided, is assumed to be a “waveguide 1”, and the waveguide including a wide core region 82, through which the TE1 is guided, is assumed to be a “waveguide 2”.
The width of the core region 81 is set to 400 nm. In this case, the width of the core region 82 is set to 838 nm so that the effective refractive indices of the TE0 of the core region 81 and the TE1 of the core region 82 are approximately the same at the wavelength of 1580 nm. The calculation result of each effective refractive index is shown in Table 1. For the calculation, a finite element method (FEM) is used.
TABLE 1TE0 of waveguide 1TE1 of waveguide 2Effective refractive index2.1788182.178940
The conversion efficiency of the asymmetric directional coupler is as follows. The conversion efficiency T is a ratio of the power of the output TE1 to the power of the input TE0.T=F sin2(qL)   (1)
Here, F and q are expressed by the following equations.
                    F        =                  1                      1            +                                          (                                  δ                  χ                                )                            2                                                          (        2        )                                q        =                                            χ              2                        +                          δ              2                                                          (        3        )            
δ is expressed by the following equation.
                    δ        =                              π            λ                    ⁢          Δ          ⁢                                          ⁢          N                                    (        4        )            
L is the length of the asymmetric directional coupler in the propagation direction of light, ΔN is an effective refractive index difference (difference between the effective refractive indices in Table 1) between the TE0 of the waveguide 1 and the TE1 of the waveguide 2 when two waveguides are independently present, and λ is a wavelength. In addition, χ is the strength of coupling of the two waveguides, and is referred to as a coupling coefficient.
In the asymmetric directional coupler, even if the effective refractive indices of the two modes to be coupled are made to be the same by adjusting the waveguide structure, such as the width of the core region, at a certain wavelength (in this example, 1580 nm), the effective refractive indices are shifted if the wavelength is changed.
This problem is a problem that does not occur in a symmetric directional coupler, in which two cores have the same height and width and the coupling of the same mode is handled, and is a problem that occurs uniquely in the asymmetric directional coupler in which the coupling of different modes is handled.
FIG. 56 shows the relationship between the wavelength and the absolute value of ΔN in the optical waveguide element of this example. From FIG. 56, it can be seen that the absolute value of ΔN increases as the wavelength is shifted from 1580 nm.
From equations (1), (2), and (4), the conversion efficiency T decreases as the wavelength is shifted. Therefore, a high efficiency of conversion in a wide wavelength band cannot be expected.
The conversion efficiency for the wavelength (1520 nm to 1640 nm) in this case was calculated based on equations (1) to (4). The result is shown in FIG. 57. In equation (1), L is a value when the minimum value of the conversion efficiency in the wavelength band (1520 nm to 1640 nm) is maximized, and L=16.1 μm.
From FIG. 57, the conversion efficiency decreases as the amount of shift from the wavelength around 1580 nm increases. In the wavelength band of 1520 nm to 1640 nm, the conversion efficiency is equal to or greater than approximately −0.94 dB. This is because the absolute value of ΔN increases with respect to the wavelength as described above.
Now, the relationship between the manufacturing error and the conversion efficiency will be described. When the waveguide structure is changed, the degree of confinement of light is changed, and the effective refractive index relevant thereto is changed. Therefore, even if the waveguide structure is designed such that the effective refractive indices of the two modes to be coupled are approximately the same at a certain wavelength, the waveguide structure is changed due to the manufacturing error and the effective refractive indices of the two modes are shifted.
As a result, conversion efficiency is reduced as in the discussion about the wavelength dependence described above.
In order to confirm this, the manufacturing error of the width of the core region caused by lithography/etching is taken as an example.
Typically, for the design value of the width of the core region (width of the core region defined by the mask; in FIG. 58, W81 and W82), a manufacturing error occurs by the same amount (δ) locally in the two core regions 81 and 82, as shown in FIG. 58. In this example, it is assumed that the positions of both side edges of each core region change by δ/2 inwardly or outwardly.
Hereinafter, a case is assumed in which a manufacturing error δ (=−30 nm) occurs in the core region 81 (design value: 400 nm in width) and the core region 82 (design value: 838 nm in width) of the optical waveguide element shown in FIGS. 55A and 55B. FIG. 59 shows the relationship between the wavelength and the absolute value of ΔN.
From FIG. 59, it can be seen that the effective refractive indices of the TE0 of the core region 81 and the TE1 of the core region 82 are greatly shifted and the absolute value of ΔN is increased. Based on this, conversion efficiency was calculated. The above-described value was adopted as L (L=16.1 μm). The result is shown in FIG. 60.
From FIG. 60, it can be seen that the conversion efficiency is greatly reduced since the absolute value of ΔN is increased due to the manufacturing error. Specifically, the conversion efficiency is approximately −5.16 dB or more at the wavelength of 1580 nm, and is approximately −7.32 dB or more in the range of 1520 nm to 1640 nm. From this, it can be said that the asymmetric directional coupler is susceptible to manufacturing errors.
Thus, the optical waveguide element including the asymmetric directional coupler in the related art has a problem that the wavelength band in mode conversion is narrow and the optical waveguide element including the asymmetric directional coupler in the related art is susceptible to manufacturing error.
The invention has been made in view of the aforementioned problem, and it is an object of the invention to provide a planar optical waveguide element that can ensure high conversion efficiency in a wide wavelength band and can ensure the efficiency of mode conversion even if the waveguide structure changes due to a manufacturing error.